Analysis of 111/999 NHS calls and 111 online reports
Quentin Leclerc, Emily Nightingale, Samuel Abbott & Thibaut Jombart, for CMMID
Saturday 06 June 2020
1 Data preparation
1.1 Outline
Load scripts: loads libraries and useful scripts used in the analyses; all
.Rfiles contained inscriptsat the root of the factory are automatically loadedLoad data: imports datasets, and may contain some ad hoc changes to the data such as specific data cleaning (not used in other reports), new variables used in the analyses, etc.
1.2 Load packages
library(reportfactory)
library(here)
library(rio)
library(tidyverse)
library(incidence)
library(distcrete)
library(epitrix)
library(earlyR)
library(projections)
library(linelist)
library(remotes)
library(janitor)
library(kableExtra)
library(DT)
library(cyphr)
library(chngpt)
library(lubridate)
library(ggpubr)
library(ggnewscale)1.3 Load scripts
These scripts will load:
- all scripts stored as
.Rfiles inside/scripts/ - all scripts stored as
.Rfiles inside/src/
These scripts also contain routines to access the latest clean encrypted data (see next section).
1.4 Load clean data
We import the latest NHS pathways data:
x <- import_pathways() %>%
as_tibble()
x
## [90m# A tibble: 133,902 x 11[39m
## site_type date sex age ccg_code ccg_name count postcode nhs_region
## [3m[90m<chr>[39m[23m [3m[90m<date>[39m[23m [3m[90m<chr>[39m[23m [3m[90m<chr>[39m[23m [3m[90m<chr>[39m[23m [3m[90m<chr>[39m[23m [3m[90m<int>[39m[23m [3m[90m<chr>[39m[23m [3m[90m<chr>[39m[23m
## [90m 1[39m 111 2020-03-18 fema… 0-18 e380000… nhs_bar… 35 rm13ae London
## [90m 2[39m 111 2020-03-18 fema… 0-18 e380000… nhs_bed… 27 mk454hr East of E…
## [90m 3[39m 111 2020-03-18 fema… 0-18 e380000… nhs_bla… 9 bb12fd North West
## [90m 4[39m 111 2020-03-18 fema… 0-18 e380000… nhs_bro… 11 br33ql London
## [90m 5[39m 111 2020-03-18 fema… 0-18 e380000… nhs_can… 9 ws111jp Midlands
## [90m 6[39m 111 2020-03-18 fema… 0-18 e380000… nhs_cit… 12 n15lz London
## [90m 7[39m 111 2020-03-18 fema… 0-18 e380000… nhs_enf… 7 en40dy London
## [90m 8[39m 111 2020-03-18 fema… 0-18 e380000… nhs_ham… 6 dl62uu North Eas…
## [90m 9[39m 111 2020-03-18 fema… 0-18 e380000… nhs_har… 24 ts232la North Eas…
## [90m10[39m 111 2020-03-18 fema… 0-18 e380000… nhs_kin… 6 kt11eu London
## [90m# … with 133,892 more rows, and 2 more variables: day [3m[90m<int>[90m[23m, weekday [3m[90m<fct>[90m[23m[39mWe also import demographics data for NHS regions in England, used later in our analysis:
path <- here::here("data", "csv", "nhs_region_population_2018.csv")
nhs_region_pop <- rio::import(path) %>%
mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))
nhs_region_pop$nhs_region <- gsub(" Of ", " of ", nhs_region_pop$nhs_region)
nhs_region_pop$nhs_region <- gsub(" And ", " and ", nhs_region_pop$nhs_region)
nhs_region_pop
## nhs_region variable value
## 1 North West 0-18 0.22538599
## 2 North East and Yorkshire 0-18 0.21876449
## 3 Midlands 0-18 0.22564656
## 4 East of England 0-18 0.22810783
## 5 London 0-18 0.23764782
## 6 South East 0-18 0.22458811
## 7 South West 0-18 0.20799797
## 8 North West 19-69 0.64274078
## 9 North East and Yorkshire 19-69 0.64437753
## 10 Midlands 19-69 0.63876675
## 11 East of England 19-69 0.63034229
## 12 London 19-69 0.67820084
## 13 South East 19-69 0.63267336
## 14 South West 19-69 0.63176131
## 15 North West 70-120 0.13187323
## 16 North East and Yorkshire 70-120 0.13685797
## 17 Midlands 70-120 0.13558669
## 18 East of England 70-120 0.14154988
## 19 London 70-120 0.08415135
## 20 South East 70-120 0.14273853
## 21 South West 70-120 0.16024072Finally, we import publically available deaths per NHS region:
dth <- import_deaths() %>%
mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))
#truncation to account for reporting delay
delay_max <- 21
dth$nhs_region <- gsub(" Of ", " of ", dth$nhs_region)
dth$nhs_region <- gsub(" And ", " and ", dth$nhs_region)
dth
## date_report nhs_region deaths
## 1 2020-03-01 East of England 0
## 2 2020-03-02 East of England 1
## 3 2020-03-03 East of England 0
## 4 2020-03-04 East of England 0
## 5 2020-03-05 East of England 0
## 6 2020-03-06 East of England 1
## 7 2020-03-07 East of England 0
## 8 2020-03-08 East of England 0
## 9 2020-03-09 East of England 1
## 10 2020-03-10 East of England 0
## 11 2020-03-11 East of England 0
## 12 2020-03-12 East of England 0
## 13 2020-03-13 East of England 1
## 14 2020-03-14 East of England 2
## 15 2020-03-15 East of England 2
## 16 2020-03-16 East of England 1
## 17 2020-03-17 East of England 1
## 18 2020-03-18 East of England 5
## 19 2020-03-19 East of England 4
## 20 2020-03-20 East of England 2
## 21 2020-03-21 East of England 11
## 22 2020-03-22 East of England 12
## 23 2020-03-23 East of England 11
## 24 2020-03-24 East of England 19
## 25 2020-03-25 East of England 26
## 26 2020-03-26 East of England 36
## 27 2020-03-27 East of England 38
## 28 2020-03-28 East of England 28
## 29 2020-03-29 East of England 43
## 30 2020-03-30 East of England 45
## 31 2020-03-31 East of England 70
## 32 2020-04-01 East of England 61
## 33 2020-04-02 East of England 64
## 34 2020-04-03 East of England 80
## 35 2020-04-04 East of England 71
## 36 2020-04-05 East of England 76
## 37 2020-04-06 East of England 71
## 38 2020-04-07 East of England 93
## 39 2020-04-08 East of England 111
## 40 2020-04-09 East of England 87
## 41 2020-04-10 East of England 74
## 42 2020-04-11 East of England 91
## 43 2020-04-12 East of England 101
## 44 2020-04-13 East of England 78
## 45 2020-04-14 East of England 61
## 46 2020-04-15 East of England 82
## 47 2020-04-16 East of England 74
## 48 2020-04-17 East of England 86
## 49 2020-04-18 East of England 64
## 50 2020-04-19 East of England 67
## 51 2020-04-20 East of England 67
## 52 2020-04-21 East of England 75
## 53 2020-04-22 East of England 67
## 54 2020-04-23 East of England 49
## 55 2020-04-24 East of England 66
## 56 2020-04-25 East of England 54
## 57 2020-04-26 East of England 48
## 58 2020-04-27 East of England 46
## 59 2020-04-28 East of England 58
## 60 2020-04-29 East of England 32
## 61 2020-04-30 East of England 44
## 62 2020-05-01 East of England 49
## 63 2020-05-02 East of England 29
## 64 2020-05-03 East of England 41
## 65 2020-05-04 East of England 19
## 66 2020-05-05 East of England 35
## 67 2020-05-06 East of England 30
## 68 2020-05-07 East of England 33
## 69 2020-05-08 East of England 33
## 70 2020-05-09 East of England 29
## 71 2020-05-10 East of England 22
## 72 2020-05-11 East of England 18
## 73 2020-05-12 East of England 21
## 74 2020-05-13 East of England 27
## 75 2020-05-14 East of England 26
## 76 2020-05-15 East of England 19
## 77 2020-05-16 East of England 26
## 78 2020-05-17 East of England 17
## 79 2020-05-18 East of England 24
## 80 2020-05-19 East of England 15
## 81 2020-05-20 East of England 26
## 82 2020-05-21 East of England 21
## 83 2020-05-22 East of England 13
## 84 2020-05-23 East of England 12
## 85 2020-05-24 East of England 16
## 86 2020-05-25 East of England 25
## 87 2020-05-26 East of England 14
## 88 2020-05-27 East of England 12
## 89 2020-05-28 East of England 17
## 90 2020-05-29 East of England 15
## 91 2020-05-30 East of England 9
## 92 2020-05-31 East of England 8
## 93 2020-06-01 East of England 14
## 94 2020-06-02 East of England 12
## 95 2020-06-03 East of England 6
## 96 2020-06-04 East of England 0
## 97 2020-03-01 London 0
## 98 2020-03-02 London 0
## 99 2020-03-03 London 0
## 100 2020-03-04 London 0
## 101 2020-03-05 London 0
## 102 2020-03-06 London 1
## 103 2020-03-07 London 1
## 104 2020-03-08 London 0
## 105 2020-03-09 London 1
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## 112 2020-03-16 London 17
## 113 2020-03-17 London 25
## 114 2020-03-18 London 31
## 115 2020-03-19 London 25
## 116 2020-03-20 London 45
## 117 2020-03-21 London 50
## 118 2020-03-22 London 54
## 119 2020-03-23 London 64
## 120 2020-03-24 London 87
## 121 2020-03-25 London 113
## 122 2020-03-26 London 130
## 123 2020-03-27 London 130
## 124 2020-03-28 London 122
## 125 2020-03-29 London 147
## 126 2020-03-30 London 150
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## 128 2020-04-01 London 202
## 129 2020-04-02 London 190
## 130 2020-04-03 London 196
## 131 2020-04-04 London 230
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## 133 2020-04-06 London 198
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## 140 2020-04-13 London 166
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## 143 2020-04-16 London 139
## 144 2020-04-17 London 99
## 145 2020-04-18 London 101
## 146 2020-04-19 London 102
## 147 2020-04-20 London 95
## 148 2020-04-21 London 95
## 149 2020-04-22 London 108
## 150 2020-04-23 London 77
## 151 2020-04-24 London 71
## 152 2020-04-25 London 57
## 153 2020-04-26 London 53
## 154 2020-04-27 London 51
## 155 2020-04-28 London 43
## 156 2020-04-29 London 44
## 157 2020-04-30 London 39
## 158 2020-05-01 London 41
## 159 2020-05-02 London 40
## 160 2020-05-03 London 36
## 161 2020-05-04 London 29
## 162 2020-05-05 London 25
## 163 2020-05-06 London 36
## 164 2020-05-07 London 37
## 165 2020-05-08 London 29
## 166 2020-05-09 London 23
## 167 2020-05-10 London 26
## 168 2020-05-11 London 18
## 169 2020-05-12 London 18
## 170 2020-05-13 London 16
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## 174 2020-05-17 London 15
## 175 2020-05-18 London 9
## 176 2020-05-19 London 13
## 177 2020-05-20 London 19
## 178 2020-05-21 London 12
## 179 2020-05-22 London 10
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## 192 2020-06-04 London 1
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## 199 2020-03-07 Midlands 0
## 200 2020-03-08 Midlands 3
## 201 2020-03-09 Midlands 1
## 202 2020-03-10 Midlands 0
## 203 2020-03-11 Midlands 2
## 204 2020-03-12 Midlands 6
## 205 2020-03-13 Midlands 5
## 206 2020-03-14 Midlands 4
## 207 2020-03-15 Midlands 5
## 208 2020-03-16 Midlands 11
## 209 2020-03-17 Midlands 8
## 210 2020-03-18 Midlands 13
## 211 2020-03-19 Midlands 8
## 212 2020-03-20 Midlands 28
## 213 2020-03-21 Midlands 13
## 214 2020-03-22 Midlands 31
## 215 2020-03-23 Midlands 33
## 216 2020-03-24 Midlands 41
## 217 2020-03-25 Midlands 48
## 218 2020-03-26 Midlands 64
## 219 2020-03-27 Midlands 72
## 220 2020-03-28 Midlands 89
## 221 2020-03-29 Midlands 92
## 222 2020-03-30 Midlands 90
## 223 2020-03-31 Midlands 123
## 224 2020-04-01 Midlands 140
## 225 2020-04-02 Midlands 142
## 226 2020-04-03 Midlands 124
## 227 2020-04-04 Midlands 151
## 228 2020-04-05 Midlands 164
## 229 2020-04-06 Midlands 140
## 230 2020-04-07 Midlands 123
## 231 2020-04-08 Midlands 186
## 232 2020-04-09 Midlands 139
## 233 2020-04-10 Midlands 127
## 234 2020-04-11 Midlands 142
## 235 2020-04-12 Midlands 139
## 236 2020-04-13 Midlands 120
## 237 2020-04-14 Midlands 116
## 238 2020-04-15 Midlands 147
## 239 2020-04-16 Midlands 102
## 240 2020-04-17 Midlands 118
## 241 2020-04-18 Midlands 115
## 242 2020-04-19 Midlands 92
## 243 2020-04-20 Midlands 107
## 244 2020-04-21 Midlands 86
## 245 2020-04-22 Midlands 78
## 246 2020-04-23 Midlands 103
## 247 2020-04-24 Midlands 79
## 248 2020-04-25 Midlands 72
## 249 2020-04-26 Midlands 81
## 250 2020-04-27 Midlands 74
## 251 2020-04-28 Midlands 68
## 252 2020-04-29 Midlands 53
## 253 2020-04-30 Midlands 56
## 254 2020-05-01 Midlands 64
## 255 2020-05-02 Midlands 51
## 256 2020-05-03 Midlands 52
## 257 2020-05-04 Midlands 61
## 258 2020-05-05 Midlands 58
## 259 2020-05-06 Midlands 59
## 260 2020-05-07 Midlands 48
## 261 2020-05-08 Midlands 34
## 262 2020-05-09 Midlands 37
## 263 2020-05-10 Midlands 41
## 264 2020-05-11 Midlands 33
## 265 2020-05-12 Midlands 45
## 266 2020-05-13 Midlands 39
## 267 2020-05-14 Midlands 36
## 268 2020-05-15 Midlands 40
## 269 2020-05-16 Midlands 34
## 270 2020-05-17 Midlands 31
## 271 2020-05-18 Midlands 34
## 272 2020-05-19 Midlands 34
## 273 2020-05-20 Midlands 36
## 274 2020-05-21 Midlands 32
## 275 2020-05-22 Midlands 26
## 276 2020-05-23 Midlands 31
## 277 2020-05-24 Midlands 19
## 278 2020-05-25 Midlands 24
## 279 2020-05-26 Midlands 31
## 280 2020-05-27 Midlands 28
## 281 2020-05-28 Midlands 26
## 282 2020-05-29 Midlands 20
## 283 2020-05-30 Midlands 19
## 284 2020-05-31 Midlands 19
## 285 2020-06-01 Midlands 18
## 286 2020-06-02 Midlands 20
## 287 2020-06-03 Midlands 16
## 288 2020-06-04 Midlands 3
## 289 2020-03-01 North East and Yorkshire 0
## 290 2020-03-02 North East and Yorkshire 0
## 291 2020-03-03 North East and Yorkshire 0
## 292 2020-03-04 North East and Yorkshire 0
## 293 2020-03-05 North East and Yorkshire 0
## 294 2020-03-06 North East and Yorkshire 0
## 295 2020-03-07 North East and Yorkshire 0
## 296 2020-03-08 North East and Yorkshire 0
## 297 2020-03-09 North East and Yorkshire 0
## 298 2020-03-10 North East and Yorkshire 0
## 299 2020-03-11 North East and Yorkshire 0
## 300 2020-03-12 North East and Yorkshire 0
## 301 2020-03-13 North East and Yorkshire 0
## 302 2020-03-14 North East and Yorkshire 0
## 303 2020-03-15 North East and Yorkshire 2
## 304 2020-03-16 North East and Yorkshire 3
## 305 2020-03-17 North East and Yorkshire 1
## 306 2020-03-18 North East and Yorkshire 2
## 307 2020-03-19 North East and Yorkshire 6
## 308 2020-03-20 North East and Yorkshire 5
## 309 2020-03-21 North East and Yorkshire 6
## 310 2020-03-22 North East and Yorkshire 7
## 311 2020-03-23 North East and Yorkshire 9
## 312 2020-03-24 North East and Yorkshire 8
## 313 2020-03-25 North East and Yorkshire 18
## 314 2020-03-26 North East and Yorkshire 21
## 315 2020-03-27 North East and Yorkshire 28
## 316 2020-03-28 North East and Yorkshire 35
## 317 2020-03-29 North East and Yorkshire 38
## 318 2020-03-30 North East and Yorkshire 64
## 319 2020-03-31 North East and Yorkshire 60
## 320 2020-04-01 North East and Yorkshire 67
## 321 2020-04-02 North East and Yorkshire 74
## 322 2020-04-03 North East and Yorkshire 100
## 323 2020-04-04 North East and Yorkshire 105
## 324 2020-04-05 North East and Yorkshire 92
## 325 2020-04-06 North East and Yorkshire 96
## 326 2020-04-07 North East and Yorkshire 102
## 327 2020-04-08 North East and Yorkshire 107
## 328 2020-04-09 North East and Yorkshire 111
## 329 2020-04-10 North East and Yorkshire 117
## 330 2020-04-11 North East and Yorkshire 98
## 331 2020-04-12 North East and Yorkshire 84
## 332 2020-04-13 North East and Yorkshire 94
## 333 2020-04-14 North East and Yorkshire 107
## 334 2020-04-15 North East and Yorkshire 96
## 335 2020-04-16 North East and Yorkshire 103
## 336 2020-04-17 North East and Yorkshire 88
## 337 2020-04-18 North East and Yorkshire 95
## 338 2020-04-19 North East and Yorkshire 88
## 339 2020-04-20 North East and Yorkshire 100
## 340 2020-04-21 North East and Yorkshire 76
## 341 2020-04-22 North East and Yorkshire 84
## 342 2020-04-23 North East and Yorkshire 62
## 343 2020-04-24 North East and Yorkshire 72
## 344 2020-04-25 North East and Yorkshire 69
## 345 2020-04-26 North East and Yorkshire 65
## 346 2020-04-27 North East and Yorkshire 65
## 347 2020-04-28 North East and Yorkshire 57
## 348 2020-04-29 North East and Yorkshire 69
## 349 2020-04-30 North East and Yorkshire 57
## 350 2020-05-01 North East and Yorkshire 64
## 351 2020-05-02 North East and Yorkshire 48
## 352 2020-05-03 North East and Yorkshire 40
## 353 2020-05-04 North East and Yorkshire 49
## 354 2020-05-05 North East and Yorkshire 40
## 355 2020-05-06 North East and Yorkshire 50
## 356 2020-05-07 North East and Yorkshire 45
## 357 2020-05-08 North East and Yorkshire 42
## 358 2020-05-09 North East and Yorkshire 44
## 359 2020-05-10 North East and Yorkshire 40
## 360 2020-05-11 North East and Yorkshire 29
## 361 2020-05-12 North East and Yorkshire 27
## 362 2020-05-13 North East and Yorkshire 28
## 363 2020-05-14 North East and Yorkshire 30
## 364 2020-05-15 North East and Yorkshire 32
## 365 2020-05-16 North East and Yorkshire 35
## 366 2020-05-17 North East and Yorkshire 26
## 367 2020-05-18 North East and Yorkshire 29
## 368 2020-05-19 North East and Yorkshire 27
## 369 2020-05-20 North East and Yorkshire 21
## 370 2020-05-21 North East and Yorkshire 33
## 371 2020-05-22 North East and Yorkshire 22
## 372 2020-05-23 North East and Yorkshire 18
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## 379 2020-05-30 North East and Yorkshire 19
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## 382 2020-06-02 North East and Yorkshire 22
## 383 2020-06-03 North East and Yorkshire 19
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## 410 2020-03-26 North West 29
## 411 2020-03-27 North West 35
## 412 2020-03-28 North West 28
## 413 2020-03-29 North West 46
## 414 2020-03-30 North West 67
## 415 2020-03-31 North West 52
## 416 2020-04-01 North West 86
## 417 2020-04-02 North West 96
## 418 2020-04-03 North West 95
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## 420 2020-04-05 North West 102
## 421 2020-04-06 North West 100
## 422 2020-04-07 North West 133
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## 424 2020-04-09 North West 119
## 425 2020-04-10 North West 117
## 426 2020-04-11 North West 138
## 427 2020-04-12 North West 126
## 428 2020-04-13 North West 127
## 429 2020-04-14 North West 131
## 430 2020-04-15 North West 114
## 431 2020-04-16 North West 134
## 432 2020-04-17 North West 97
## 433 2020-04-18 North West 113
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## 469 2020-05-24 North West 26
## 470 2020-05-25 North West 31
## 471 2020-05-26 North West 27
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## 533 2020-04-22 South East 54
## 534 2020-04-23 South East 57
## 535 2020-04-24 South East 64
## 536 2020-04-25 South East 51
## 537 2020-04-26 South East 51
## 538 2020-04-27 South East 40
## 539 2020-04-28 South East 40
## 540 2020-04-29 South East 47
## 541 2020-04-30 South East 29
## 542 2020-05-01 South East 37
## 543 2020-05-02 South East 36
## 544 2020-05-03 South East 17
## 545 2020-05-04 South East 35
## 546 2020-05-05 South East 29
## 547 2020-05-06 South East 25
## 548 2020-05-07 South East 26
## 549 2020-05-08 South East 26
## 550 2020-05-09 South East 28
## 551 2020-05-10 South East 19
## 552 2020-05-11 South East 25
## 553 2020-05-12 South East 27
## 554 2020-05-13 South East 18
## 555 2020-05-14 South East 32
## 556 2020-05-15 South East 24
## 557 2020-05-16 South East 22
## 558 2020-05-17 South East 17
## 559 2020-05-18 South East 22
## 560 2020-05-19 South East 12
## 561 2020-05-20 South East 22
## 562 2020-05-21 South East 14
## 563 2020-05-22 South East 17
## 564 2020-05-23 South East 19
## 565 2020-05-24 South East 16
## 566 2020-05-25 South East 13
## 567 2020-05-26 South East 17
## 568 2020-05-27 South East 17
## 569 2020-05-28 South East 12
## 570 2020-05-29 South East 17
## 571 2020-05-30 South East 8
## 572 2020-05-31 South East 10
## 573 2020-06-01 South East 10
## 574 2020-06-02 South East 7
## 575 2020-06-03 South East 11
## 576 2020-06-04 South East 1
## 577 2020-03-01 South West 0
## 578 2020-03-02 South West 0
## 579 2020-03-03 South West 0
## 580 2020-03-04 South West 0
## 581 2020-03-05 South West 0
## 582 2020-03-06 South West 0
## 583 2020-03-07 South West 0
## 584 2020-03-08 South West 0
## 585 2020-03-09 South West 0
## 586 2020-03-10 South West 0
## 587 2020-03-11 South West 1
## 588 2020-03-12 South West 0
## 589 2020-03-13 South West 0
## 590 2020-03-14 South West 1
## 591 2020-03-15 South West 0
## 592 2020-03-16 South West 0
## 593 2020-03-17 South West 2
## 594 2020-03-18 South West 2
## 595 2020-03-19 South West 5
## 596 2020-03-20 South West 3
## 597 2020-03-21 South West 6
## 598 2020-03-22 South West 9
## 599 2020-03-23 South West 9
## 600 2020-03-24 South West 7
## 601 2020-03-25 South West 9
## 602 2020-03-26 South West 11
## 603 2020-03-27 South West 13
## 604 2020-03-28 South West 21
## 605 2020-03-29 South West 18
## 606 2020-03-30 South West 23
## 607 2020-03-31 South West 23
## 608 2020-04-01 South West 22
## 609 2020-04-02 South West 23
## 610 2020-04-03 South West 30
## 611 2020-04-04 South West 42
## 612 2020-04-05 South West 32
## 613 2020-04-06 South West 34
## 614 2020-04-07 South West 39
## 615 2020-04-08 South West 47
## 616 2020-04-09 South West 24
## 617 2020-04-10 South West 46
## 618 2020-04-11 South West 43
## 619 2020-04-12 South West 23
## 620 2020-04-13 South West 27
## 621 2020-04-14 South West 24
## 622 2020-04-15 South West 32
## 623 2020-04-16 South West 29
## 624 2020-04-17 South West 33
## 625 2020-04-18 South West 25
## 626 2020-04-19 South West 31
## 627 2020-04-20 South West 26
## 628 2020-04-21 South West 26
## 629 2020-04-22 South West 22
## 630 2020-04-23 South West 17
## 631 2020-04-24 South West 19
## 632 2020-04-25 South West 15
## 633 2020-04-26 South West 27
## 634 2020-04-27 South West 13
## 635 2020-04-28 South West 17
## 636 2020-04-29 South West 15
## 637 2020-04-30 South West 26
## 638 2020-05-01 South West 6
## 639 2020-05-02 South West 7
## 640 2020-05-03 South West 10
## 641 2020-05-04 South West 16
## 642 2020-05-05 South West 14
## 643 2020-05-06 South West 18
## 644 2020-05-07 South West 16
## 645 2020-05-08 South West 6
## 646 2020-05-09 South West 11
## 647 2020-05-10 South West 5
## 648 2020-05-11 South West 8
## 649 2020-05-12 South West 7
## 650 2020-05-13 South West 7
## 651 2020-05-14 South West 6
## 652 2020-05-15 South West 4
## 653 2020-05-16 South West 4
## 654 2020-05-17 South West 6
## 655 2020-05-18 South West 4
## 656 2020-05-19 South West 6
## 657 2020-05-20 South West 1
## 658 2020-05-21 South West 9
## 659 2020-05-22 South West 6
## 660 2020-05-23 South West 6
## 661 2020-05-24 South West 3
## 662 2020-05-25 South West 7
## 663 2020-05-26 South West 11
## 664 2020-05-27 South West 5
## 665 2020-05-28 South West 8
## 666 2020-05-29 South West 4
## 667 2020-05-30 South West 3
## 668 2020-05-31 South West 2
## 669 2020-06-01 South West 6
## 670 2020-06-02 South West 2
## 671 2020-06-03 South West 4
## 672 2020-06-04 South West 11.5 Completion date
We extract the completion date from the NHS Pathways file timestamp:
The completion date of the NHS Pathways data is Thursday 04 Jun 2020.
1.6 Auxiliary functions
These are functions which will be used further in the analyses.
Function to estimate the generalised R-squared as the proportion of deviance explained by a given model:
## Function to calculate R2 for Poisson model
## not adjusted for model complexity but all models have the same DF here
Rsq <- function(x) {
1 - (x$deviance / x$null.deviance)
}Function to extract growth rates per region as well as halving times, and the associated 95% confidence intervals:
## function to extract the coefficients, find the level of the intercept,
## reconstruct the values of r, get confidence intervals
get_r <- function(model) {
## extract coefficients and conf int
out <- data.frame(r = coef(model)) %>%
rownames_to_column("var") %>%
cbind(confint(model)) %>%
filter(!grepl("day_of_week", var)) %>%
filter(grepl("day", var)) %>%
rename(lower_95 = "2.5 %",
upper_95 = "97.5 %") %>%
mutate(var = sub("day:", "", var))
## reconstruct values: intercept + region-coefficient
for (i in 2:nrow(out)) {
out[i, -1] <- out[1, -1] + out[i, -1]
}
## find the name of the intercept, restore regions names
out <- out %>%
mutate(nhs_region = model$xlevels$nhs_region) %>%
select(nhs_region, everything(), -var)
## find halving times
halving <- log(0.5) / out[,-1] %>%
rename(halving_t = r,
halving_t_lower_95 = lower_95,
halving_t_upper_95 = upper_95)
## set halving times with exclusion intervals to NA
no_halving <- out$lower_95 < 0 & out$upper_95 > 0
halving[no_halving, ] <- NA_real_
## return all data
cbind(out, halving)
}Functions used in the correlation analysis between NHS Pathways reports and deaths:
## Function to calculate Pearson's correlation between deaths and lagged
## reports. Note that `pearson` can be replaced with `spearman` for rank
## correlation.
getcor <- function(x, ndx) {
return(cor(x$deaths[ndx],
x$note_lag[ndx],
use = "complete.obs",
method = "pearson"))
}
## Catch if sample size throws an error
getcor2 <- possibly(getcor, otherwise = NA)
getboot <- function(x) {
result <- boot::boot.ci(boot::boot(x, getcor2, R = 1000),
type = "bca")
return(data.frame(n = sum(!is.na(x$note_lag) & !is.na(x$deaths)),
r = result$t0,
r_low = result$bca[4],
r_hi = result$bca[5]))
}Function to classify the day of the week into weekend, Monday, and the rest:
## Fn to add day of week
day_of_week <- function(df) {
df %>%
dplyr::mutate(day_of_week = lubridate::wday(date, label = TRUE)) %>%
dplyr::mutate(day_of_week = dplyr::case_when(
day_of_week %in% c("Sat", "Sun") ~ "weekend",
day_of_week %in% c("Mon") ~ "monday",
!(day_of_week %in% c("Sat", "Sun", "Mon")) ~ "rest_of_week"
) %>%
factor(levels = c("rest_of_week", "monday", "weekend")))
}Custom color palettes, color scales, and vectors of colors:
2 Temporal trends in NHS Pathways reports
2.1 Outline
We look for temporal patterns in COVID-19 related 111/999 calls and 111 online reports. Analyses are broken down by NHS region. We also look for estimates of recent growth rate and associated doubling / halving time.
2.2 Reports by region over time
tab_date_region_all <- x %>%
filter(!is.na(nhs_region)) %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
dth %>%
mutate(trusted = case_when(date_report < max(dth$date_report)-delay_max ~ "Y",
date_report >= max(dth$date_report)-delay_max ~ "N"),
value = "Deaths",
vline = max(dth$date_report)-delay_max-1,
lab = "Truncated for reporting delay",
lab_pos_x = vline + 8,
lab_pos_y = 150,
lab_col = "darkgrey") %>%
rename(date = date_report,
n = deaths) %>%
bind_rows(
mutate(tab_date_region_all, value = "Reports",
trusted = "Y",
vline = as.Date("2020-03-23"),
lab = "Start of UK lockdown",
lab_pos_x = vline - 6,
lab_pos_y = 30000,
lab_col = "black")
) %>%
mutate(value = factor(value, levels = c("Reports","Deaths"))) -> dths_reports
plot_dth_report <-
ggplot(dths_reports, aes(date, n, colour = nhs_region)) +
# Add main points and lines, coloured by region and fade out deaths for excluded period
geom_point(aes(alpha = trusted)) +
geom_line(alpha = 0.2) +
geom_smooth(method = "loess", span = .5, color = "black") +
scale_colour_manual("", values = pal) +
scale_alpha_manual(values = c(0.3,1)) +
guides(alpha = F) +
# Add vertical markers for important dates with labels - different for each facet
ggnewscale::new_scale_colour() +
geom_vline(aes(xintercept = vline, col = value), lty = "solid") +
geom_text(aes(x = lab_pos_x, y = lab_pos_y, label = lab, col = value), size = 3) +
scale_colour_manual("",values = c("black","darkgrey"), guide = F) +
# Facet by deaths and reports
facet_grid(rows = vars(value), scales = "free_y", switch = "y") +
# Other formatting
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",strip.placement = "outside") +
rotate_x +
labs(x = NULL,
y = NULL)
plot_dth_report
2.3 Reports by region by age over time
We plot the number of 111/999 calls and 111 online reports by age, and the proportion of 111/999 calls and 111 online reports by age. In the second graph, the vertical lines indicate the proportion of individuals residing in the corresponding NHS region who belong to the corresponding age group.
tab_date_region_age_all <- x %>%
filter(!is.na(nhs_region),
age != "missing") %>%
group_by(date, nhs_region, age) %>%
summarise(n = sum(count))
tab_date_region_age_all %>%
ggplot(aes(x = date, y = n, fill = age)) +
geom_col(position = "stack") +
scale_fill_manual(values = age.pal) +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
axis.text.x = element_text(angle = 90, hjust = 1)) +
guides(fill = guide_legend(title = "Age", ncol = 3)) +
labs(x = NULL,
y = "Total daily reports by age") +
facet_wrap(~ nhs_region, ncol = 4)
tab_date_region_age_all <- tab_date_region_age_all %>%
group_by(date, nhs_region) %>%
summarise(tot = sum(n)) %>%
left_join(tab_date_region_age_all, by = c("date", "nhs_region")) %>%
mutate(prop_n = n/tot)
tab_date_region_age_all %>%
ggplot(aes(x = date, y = prop_n, color = age)) +
scale_color_manual(values = age.pal) +
geom_line() +
geom_point() +
geom_hline(data = nhs_region_pop, aes(yintercept = value, color = variable)) +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
axis.text.x = element_text(angle = 90, hjust = 1)) +
guides(color = guide_legend(title = "Age", ncol = 3)) +
labs(x = NULL,
y = "Proportion of daily reports by age") +
facet_wrap(~ nhs_region, ncol = 4)
2.4 Moving window model
We fit quasi-Poisson GLMs for 14-day windows to get growth rates over time.
## set moving time window (1/2/3 weeks)
w <- 14
# create empty df
r_all_sliding <- NULL
## make data for model
x_model_all_moving <- x %>%
filter(!is.na(nhs_region)) %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding <- bind_rows(r_all_sliding, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale,
w = 0.5)
#convert growth rates r to R0
r_all_sliding <- r_all_sliding %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))We examine the evolution of the growth rate by region over time.
# plot
plot_growth <-
r_all_sliding %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)") +
scale_colour_manual(values = pal)From the growth rate, we derive R and examine its value through time.
# plot
plot_R <-
r_all_sliding %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)") +
scale_colour_manual(values = pal)
R <- r_all_sliding %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
# strip.text.x = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "",
override.aes = list(fill = NA)),
fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)")))
2.5 Moving window model - stratified by age
We repeat the above analysis, where we fit quasi-Poisson GLMs for 14-day windows to get growth rates over time, but apply this to each age group separately (0-18, 19-69, 70-120 years old).
We first run the analysis for 0-18 years old.
## set moving time window (2 weeks)
w <- 14
# create empty df
r_all_sliding_0_18 <- NULL
## make data for model
x_model_all_moving_0_18 <- x %>%
filter(!is.na(nhs_region),
age == "0-18") %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving_0_18$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving_0_18 %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding_0_18 <- bind_rows(r_all_sliding_0_18, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale, w = 0.5)
#convert growth rates r to R0
r_all_sliding_0_18 <- r_all_sliding_0_18 %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))# plot
plot_growth <-
r_all_sliding_0_18 %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)"
) +
scale_colour_manual(values = pal)# plot
plot_R <-
r_all_sliding_0_18 %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)"
) +
scale_colour_manual(values = pal)
R <- r_all_sliding_0_18 %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding_0_18 %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
fig2_3_0_18 <- r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)")))Then, we run the analysis for 19-69 years old.
## set moving time window (2 weeks)
w <- 14
# create empty df
r_all_sliding_19_69 <- NULL
## make data for model
x_model_all_moving_19_69 <- x %>%
filter(!is.na(nhs_region),
age == "19-69") %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving_19_69$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving_19_69 %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding_19_69 <- bind_rows(r_all_sliding_19_69, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale, w = 0.5)
#convert growth rates r to R0
r_all_sliding_19_69 <- r_all_sliding_19_69 %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))# plot
plot_growth <-
r_all_sliding_19_69 %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)") +
scale_colour_manual(values = pal)# plot
plot_R <-
r_all_sliding_19_69 %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)"
) +
scale_colour_manual(values = pal)
R <- r_all_sliding_19_69 %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding_19_69 %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
fig2_3_19_69 <- r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)")))Finally, we run the analysis for 70-120 years old.
## set moving time window (2 weeks)
w <- 14
# create empty df
r_all_sliding_70_120 <- NULL
## make data for model
x_model_all_moving_70_120 <- x %>%
filter(!is.na(nhs_region),
age == "70-120") %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving_70_120$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving_70_120 %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding_70_120 <- bind_rows(r_all_sliding_70_120, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale, w = 0.5)
#convert growth rates r to R0
r_all_sliding_70_120 <- r_all_sliding_70_120 %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))# plot
plot_growth <-
r_all_sliding_70_120 %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)"
) +
scale_colour_manual(values = pal)# plot
plot_R <-
r_all_sliding_70_120 %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)") +
scale_colour_manual(values = pal)
R <- r_all_sliding_70_120 %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding_70_120 %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
fig2_3_70_120 <- r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)"))) We combine the estimated growth rates and effective reproduction numbers into a single figure.
ggpubr::ggarrange(fig2_3_0_18,
fig2_3_19_69,
fig2_3_70_120,
nrow = 3,
labels = "AUTO",
common.legend = TRUE,
legend = "bottom",
align = "hv") 
3 Comparison with deaths time series
3.1 Outline
We want to explore the correlation between NHS Pathways reports and deaths, and assess the potential for reports to be used as an early warning system for disease resurgence.
Death data are publically available. We truncate the time series to avoid bias from reporting delay - we assume a conservative delay of three weeks.
3.2 Lagged correlation
We calculate Pearson’s correlation coefficient between deaths and NHS Pathways notifications using different lags. Confidence intervals are obtained using bootstrap. Note that results were also confirmed using Spearman’s rank correlation.
First we join the NHS Pathways and death data, and aggregate over all England:
## truncate death data for reporting delay
trunc_date <- max(dth$date_report) - delay_max
dth_trunc <- dth %>%
rename(date = date_report) %>%
filter(date <= trunc_date)
## join with notification data
all_data <- x %>%
filter(!is.na(nhs_region)) %>%
group_by(date, nhs_region) %>%
summarise(count = sum(count, na.rm = T)) %>%
ungroup %>%
inner_join(dth_trunc,
by = c("date","nhs_region"))
all_tot <- all_data %>%
group_by(date) %>%
summarise(count = sum(count, na.rm = TRUE),
deaths = sum(deaths, na.rm = TRUE)) We calculate correlation with lagged NHS Pathways reports from 0 to 30 days behind deaths:
## Calculate all correlations + bootstrap CIs
lag_cor <- data.frame()
for (i in 0:30) {
## lag reports
summary <- all_tot %>%
mutate(note_lag = lag(count, i)) %>%
## calculate rank correlation and bootstrap CI
getboot(.) %>%
mutate(lag = i)
lag_cor <- bind_rows(lag_cor, summary)
}
cor_vs_lag <- ggplot(lag_cor, aes(lag, r)) +
theme_bw() +
geom_ribbon(aes(ymin = r_low, ymax = r_hi), alpha = 0.2) +
geom_hline(yintercept = 0, lty = "longdash") +
geom_point() +
geom_line() +
labs(x = "Lag between NHS pathways and death data (days)",
y = "Pearson's correlation") +
large_txt
cor_vs_lag
This analysis suggests that the best lag is 23 days. We then compare and plot the number of deaths reported against the number of NHS Pathways reports lagged by 23 days.
all_tot <- all_tot %>%
rename(date_death = date) %>%
mutate(note_lag = lag(count, lag_cor$lag[l_opt]),
note_lag_c = (note_lag - mean(note_lag, na.rm = T)),
date_note = lag(date_death,16))
lag_mod <- glm(deaths ~ note_lag, data = all_tot, family = "quasipoisson")
summary(lag_mod)
##
## Call:
## glm(formula = deaths ~ note_lag, family = "quasipoisson", data = all_tot)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -7.3346 -1.8851 0.4508 1.6690 4.6278
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.154e+00 5.229e-02 98.57 <2e-16 ***
## note_lag 9.943e-06 4.942e-07 20.12 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for quasipoisson family taken to be 6.914769)
##
## Null deviance: 3066.44 on 34 degrees of freedom
## Residual deviance: 234.37 on 33 degrees of freedom
## (23 observations deleted due to missingness)
## AIC: NA
##
## Number of Fisher Scoring iterations: 4
exp(coefficients(lag_mod))
## (Intercept) note_lag
## 173.12821 1.00001
exp(confint(lag_mod))
## 2.5 % 97.5 %
## (Intercept) 156.114190 191.631534
## note_lag 1.000009 1.000011
Rsq(lag_mod)
## [1] 0.9235702
mod_fit <- as.data.frame(predict(lag_mod, type = "link", se.fit = TRUE)[1:2])
all_tot_pred <-
all_tot %>%
filter(!is.na(note_lag)) %>%
mutate(pred = mod_fit$fit,
pred.se = mod_fit$se.fit,
low = exp(pred - 1.96*pred.se),
hi = exp(pred + 1.96*pred.se))
glm_fit <- all_tot_pred %>%
filter(!is.na(note_lag)) %>%
ggplot(aes(x = note_lag, y = deaths)) +
geom_point() +
geom_line(aes(y = exp(pred))) +
geom_ribbon(aes(ymin = low, ymax = hi), alpha = 0.3, col = "grey") +
theme_bw() +
labs(y = "Daily number of\ndeaths reported",
x = "Daily number of NHS Pathways reports") +
large_txt
glm_fit
4 Supplementary figures
4.1 Serial interval distribution
This is a comparison of gamma versus lognormal distribution for the serial interval used to convert r to R in our analysis. Both distributions are parameterised with mean 4.7 and standard deviation 2.9.
SI_param <- epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale, w = 0.5)
SI_distribution2 <- distcrete::distcrete("lnorm", interval = 1,
meanlog = log(4.7),
sdlog = log(2.9), w = 0.5)
SI_dist1 <- data.frame(x = SI_distribution$r(1e5))
SI_dist1 <- count(SI_dist1, x) %>%
ggplot() +
geom_col(aes(x = x, y = n)) +
labs(x = "Serial interval (days)", y = "Frequency") +
scale_x_continuous(breaks = seq(0, 30, 5)) +
theme_bw()
SI_dist2 <- data.frame(x = SI_distribution2$r(1e5))
SI_dist2 <- count(SI_dist2, x) %>%
ggplot() +
geom_col(aes(x = x, y = n)) +
labs(x = "Serial interval (days)", y = "Frequency") +
scale_x_continuous(breaks = seq(0, 200, 20), limits = c(0, 200)) +
theme_bw()
ggpubr::ggarrange(SI_dist1,
SI_dist2,
nrow = 1,
labels = "AUTO") 
4.2 Sensitivity analysis - 7 or 21 days moving window
We reproduce the window analysis with either a 7 or 21 days window for sensitivity purposes.
First with the 7 days window:
## set moving time window (1/2/3 weeks)
w <- 7
# create empty df
r_all_sliding_7days <- NULL
## make data for model
x_model_all_moving <- x %>%
filter(!is.na(nhs_region)) %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding_7days <- bind_rows(r_all_sliding_7days, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale,
w = 0.5)
#convert growth rates r to R0
r_all_sliding_7days <- r_all_sliding_7days %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))# plot
plot_growth <-
r_all_sliding_7days %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)") +
scale_colour_manual(values = pal)plot_R <- r_all_sliding_7days %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)") +
scale_colour_manual(values = pal)
R <- r_all_sliding_7days %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding_7days %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
r_R_7 <- r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)")))Then with the 21 days window:
## set moving time window (1/2/3 weeks)
w <- 21
# create empty df
r_all_sliding_21days <- NULL
## make data for model
x_model_all_moving <- x %>%
filter(!is.na(nhs_region)) %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding_21days <- bind_rows(r_all_sliding_21days, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale,
w = 0.5)
#convert growth rates r to R0
r_all_sliding_21days <- r_all_sliding_21days %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))# plot
plot_growth <-
r_all_sliding_21days %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)") +
scale_colour_manual(values = pal)# plot
plot_R <-
r_all_sliding_21days %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)") +
scale_colour_manual(values = pal)
R <- r_all_sliding_21days %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding_21days %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
r_R_21 <- r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)")))And we combine both outputs into a single plot:
ggpubr::ggarrange(r_R_7,
r_R_21,
nrow = 2,
labels = "AUTO",
common.legend = TRUE,
legend = "bottom") 
4.3 Correlation between NHS Pathways reports and deaths by NHS region
lag_cor_reg <- data.frame()
for (i in 0:30) {
summary <-
all_data %>%
group_by(nhs_region) %>%
mutate(note_lag = lag(count, i)) %>%
## calculate rank correlation and bootstrap CI for each region
group_modify(~getboot(.x)) %>%
mutate(lag = i)
lag_cor_reg <- bind_rows(lag_cor_reg, summary)
}
cor_vs_lag_reg <-
lag_cor_reg %>%
ggplot(aes(lag, r, col = nhs_region)) +
geom_hline(yintercept = 0, lty = "longdash") +
geom_ribbon(aes(ymin = r_low, ymax = r_hi, col = NULL, fill = nhs_region), alpha = 0.2) +
geom_point() +
geom_line() +
facet_wrap(~nhs_region) +
scale_color_manual(values = pal) +
scale_fill_manual(values = pal, guide = F) +
theme_bw() +
labs(x = "Lag between NHS pathways and death data (days)", y = "Pearson's correlation", col = "NHS region") +
theme(legend.position = "bottom") +
guides(color = guide_legend(override.aes = list(fill = NA)))
cor_vs_lag_reg
5 Export data
We save the tables created during our analysis:
if (!dir.exists("excel_tables")) {
dir.create("excel_tables")
}
## list all tables, and loop over export
tables_to_export <- c("r_all_sliding", "lag_cor")
for (e in tables_to_export) {
rio::export(get(e),
file.path("excel_tables",
paste0(e, ".xlsx")))
}
## also export result from regression on lagged data
rio::export(lag_mod, file.path("excel_tables", "lag_mod.rds"))6 System information
6.1 Outline
The following information documents the system on which the document was compiled.
6.2 System
This provides information on the operating system.
6.3 R environment
This provides information on the version of R used:
6.4 R packages
This provides information on the packages used:
sessionInfo()
## R version 3.6.3 (2020-02-29)
## Platform: x86_64-apple-darwin15.6.0 (64-bit)
## Running under: macOS Catalina 10.15.5
##
## Matrix products: default
## BLAS: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRlapack.dylib
##
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] ggnewscale_0.4.1 ggpubr_0.3.0 lubridate_1.7.8
## [4] chngpt_2020.5-21 cyphr_1.1.0 DT_0.13
## [7] kableExtra_1.1.0 janitor_2.0.1 remotes_2.1.1
## [10] projections_0.4.1 earlyR_0.0.1 epitrix_0.2.2
## [13] distcrete_1.0.3 incidence_1.7.1 rio_0.5.16
## [16] reshape2_1.4.4 rvest_0.3.5 xml2_1.3.2
## [19] linelist_0.0.40.9000 forcats_0.5.0 stringr_1.4.0
## [22] dplyr_1.0.0 purrr_0.3.4 readr_1.3.1
## [25] tidyr_1.1.0 tibble_3.0.1 ggplot2_3.3.1
## [28] tidyverse_1.3.0 here_0.1 reportfactory_0.0.5
##
## loaded via a namespace (and not attached):
## [1] colorspace_1.4-1 selectr_0.4-2 ggsignif_0.6.0 ellipsis_0.3.1
## [5] rprojroot_1.3-2 snakecase_0.11.0 fs_1.4.1 rstudioapi_0.11
## [9] farver_2.0.3 fansi_0.4.1 splines_3.6.3 knitr_1.28
## [13] jsonlite_1.6.1 broom_0.5.6 dbplyr_1.4.4 compiler_3.6.3
## [17] httr_1.4.1 backports_1.1.7 assertthat_0.2.1 Matrix_1.2-18
## [21] cli_2.0.2 htmltools_0.4.0 prettyunits_1.1.1 tools_3.6.3
## [25] gtable_0.3.0 glue_1.4.1 Rcpp_1.0.4.6 carData_3.0-4
## [29] cellranger_1.1.0 vctrs_0.3.1 nlme_3.1-144 matchmaker_0.1.1
## [33] crosstalk_1.1.0.1 xfun_0.14 ps_1.3.3 openxlsx_4.1.5
## [37] lifecycle_0.2.0 rstatix_0.5.0 MASS_7.3-51.5 scales_1.1.1
## [41] hms_0.5.3 sodium_1.1 yaml_2.2.1 curl_4.3
## [45] gridExtra_2.3 stringi_1.4.6 kyotil_2019.11-22 boot_1.3-24
## [49] pkgbuild_1.0.8 zip_2.0.4 rlang_0.4.6 pkgconfig_2.0.3
## [53] evaluate_0.14 lattice_0.20-38 labeling_0.3 htmlwidgets_1.5.1
## [57] cowplot_1.0.0 processx_3.4.2 tidyselect_1.1.0 plyr_1.8.6
## [61] magrittr_1.5 R6_2.4.1 generics_0.0.2 DBI_1.1.0
## [65] pillar_1.4.4 haven_2.3.1 foreign_0.8-75 withr_2.2.0
## [69] mgcv_1.8-31 survival_3.1-8 abind_1.4-5 modelr_0.1.8
## [73] crayon_1.3.4 car_3.0-8 utf8_1.1.4 rmarkdown_2.2
## [77] viridis_0.5.1 grid_3.6.3 readxl_1.3.1 data.table_1.12.8
## [81] blob_1.2.1 callr_3.4.3 reprex_0.3.0 digest_0.6.25
## [85] webshot_0.5.2 munsell_0.5.0 viridisLite_0.3.0